Tag: nuclei

Questions Related to nuclei

Name the following nuclear reaction :
$ _{92}U^{238}(\alpha, 6p, 13n) _{88}Ra^{228}$

nuclear reactions nuclear structure nuclei atomic nuclei physics

  1. particle-particle reaction

  2. capture reaction

  3. fission reaction

  4. separation

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Correct Option: D

Consider a hypothetical annihilation of a stationary electron with a stationary positron. What is the wavelength of the resulting radiation?

nuclear reactions nuclear structure nuclei atomic nuclei physics

  1. $\lambda = \displaystyle\frac{h}{2m _ec}$

  2. $\lambda = \displaystyle\frac{2h}{m _ec^2}$

  3. $\lambda = \displaystyle\frac{h}{2m _ec^2}$

  4. None of these

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Correct Option: A
Explanation:

Annihilation is the conversion of matter into energy.
Using equation $E={ m } _{ e }{ c }^{ 2 }$
$\dfrac { hc }{ \lambda  } =2{ m } _{ e }{ c }^{ 2 }$
$\Rightarrow \lambda =\dfrac { h }{ { 2m } _{ e }{ c } } $

In which of the following nuclear reactions, the product is incorrectly matched ?

nuclear reactions nuclear structure nuclei atomic nuclei physics

  1. $ _{96}Cm^{242}(\alpha, 2n) _{97}Bk^{243}$

  2. $ _5B^{10}(\alpha, n) _7N^{13}$

  3. $ _7N^{14}(n, p) _6C^{14}$

  4. $ _{14}Si^{28}(d, n) _{15}P^{29}$

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Correct Option: A

A proton and an alpha particle having same momentum enter a magnetic field at right angles to it. If $r _1$ and $r _2$ be their radii respectively then value of $r _1 /r _2$ is : 

nuclear reactions nuclear structure nuclei atomic nuclei physics

  1. $1$

  2. $2$

  3. $1/2$

  4. $1/4$

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Correct Option: B

$A5\times 10^{-4}\overset {o}{A}$ photon produces an electron-positron pair in the vicinity of a heavy nucleus. Rest energy of electron is 0.5 11 MeV. If they have the same kinetic energies, the energy of each particle is nearly

nuclear reactions nuclear structure nuclei atomic nuclei physics

  1. 1.2 MeV

  2. 12 MeV

  3. 120 MeV

  4. 1200 MeV

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Correct Option: B

If mass-energy equivalence is taken into account, when water is cooled to form ice, the mass of water should

nuclear reactions nuclear structure nuclei atomic nuclei physics

  1. increase

  2. remain unchanged

  3. decrease

  4. first increase then decrease

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Correct Option: A
Explanation:

Because thermal energy decreases, therefore mass should increase.

If 1mg of ${ U }^{ 235 }$ is completely annihilated, the energy liberated is

nuclear reactions nuclear structure nuclei atomic nuclei physics

  1. $\quad 9\times { 10 }^{ 10 } J$

  2. $\quad 9\times { 10 }^{ 19} J$

  3. $\quad 9\times { 10 }^{ 18} J$

  4. $\quad 9\times { 10 }^{ 17} J$

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Correct Option: A
Explanation:

$E={ mc }^{ 2 }={ 10 }^{ -6 }\times \left( 3\times { 10 }^{ 8 } \right) ^{ 2 }={ 10 }^{ -6 }\times 9\times { 10 }^{ 16 }=9\times { 10 }^{ 10 }J$

One milligram of matter convert into energy will give

nuclear reactions nuclear structure nuclei atomic nuclei physics

  1. $90 joule$

  2. $9\times { 10 }^{ 3} joule$

  3. $9\times { 10 }^{ 5} joule$

  4. $9\times { 10 }^{ 10} joule$

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Correct Option: D
Explanation:

$E={ mc }^{ 2 }={ 10 }^{ -3 }\times{ 10 }^{ -3 } \left( 3\times { 10 }^{ 8 } \right) ^{ 2 }=9\times { 10 }^{ 10 }J$

The mass and energy equivalent to $1 amu$ are respectively

nuclear reactions nuclear structure nuclei atomic nuclei physics

  1. $1.67\times { 10 }^{ -27 }gm$, $9.30 MeV$

  2. $1.67\times { 10 }^{ -27 }kg$, $930 MeV$

  3. $1.67\times { 10 }^{ -27 }kg$,$ 1 MeV$

  4. $1.67\times { 10 }^{ -34 }kg$, $1 MeV$

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Correct Option: B
Explanation:

1 amu
It is defined as one twelfth of the mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state.


Mass of 1 mole C atoms $= 12 gms$
$1\ amu = $$ \cfrac{12}{12 \times 6.023 \times 10^{23}} = 1.66 \times 10^{-27} kg$

Energy equivalent, $E = mc^2 =1.66 \times 10^{-27} kg \times (3 \times 10^8)^2$$ = 930\ MeV$

If an electron and positron annihilate, then the energy released is

nuclear reactions nuclear structure nuclei atomic nuclei physics

  1. $3.2\times { 10 }^{ -13 } J$

  2. $1.6\times { 10 }^{ -13 } J$

  3. $4.8\times { 10 }^{ -13 } J$

  4. $6.4\times { 10 }^{ -13 } J$

Show answer
Correct Option: B
Explanation:

Energy of electron $={ m } _{ e }{ c }^{ 2 }$
Energy of positron $={ m } _{ p }{ c }^{ 2 }$
${ m } _{ e }$ = ${ m } _{ p }$, $ c=$ speed of light.

Thus according to conservation of energy released $=2{ m } _{ e }{ c }^{ 2 }$$=2\times 9.1\times { 10 }^{ -31 }\left( 3\times { 10 }^{ 8 } \right) ^{ 2 }=1.6\times { 10 }^{ -13 } Joules.$